Truncated Wigner approximation as a non-positive Kraus map

We show that the Truncated Wigner Approximation developed in the flat phase-space is mapped into a Lindblad-type evolution with an indefinite metric in the space of linear operators. As a result, the classically evolved Wigner function corresponds to a non-positive operator \(\hat{R}(t)\), which doe...

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Bibliographic Details
Published in:	arXiv.org
Main Authors:	Klimov, A B, Sainz, I, Romero, J L
Format:	Paper
Language:	English
Published:	Ithaca Cornell University Library, arXiv.org 09.08.2021
Subjects:	Approximation Eigenvalues Evolution Linear operators Mathematical analysis Second harmonic generation
ISSN:	2331-8422
Online Access:	Get full text
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Summary:	We show that the Truncated Wigner Approximation developed in the flat phase-space is mapped into a Lindblad-type evolution with an indefinite metric in the space of linear operators. As a result, the classically evolved Wigner function corresponds to a non-positive operator \(\hat{R}(t)\), which does not describe a physical state. The rate of appearance of negative eigenvalues of \(\hat{R}(t)\) can be efficiently estimated. The short-time dynamics of the Kerr and second harmonic generation Hamiltonains are discussed.
Bibliography:	SourceType-Working Papers-1 ObjectType-Working Paper/Pre-Print-1 content type line 50
ISSN:	2331-8422
DOI:	10.48550/arxiv.2108.04189